More: On Monday, Donald Trump said the war on Iran was "very complete".

On Tuesday, Pete Hegseth, his secretary of defence, said Iran would face "the most intense day of strikes" yet in Operation Epic Fury.

If the messaging seems confused, it may be because the US " and to a lesser extent Israel " has found itself caught in a classic military trap. By relying on overwhelming firepower, they have been suckered into what could yet prove to be another Vietnam.

There, the US won every battle over 11 bloody years, but famously lost the war.

This was despite it, as now, having complete air superiority, and quickly destroying most of the crucial military and industrial infrastructure on which the enemy was thought to rely.

By escalating the Vietnam War "horizontally" into the towns and cities in the south on their own terms, the North Vietnamese and Vietcong forces outmanoeuvred the US.

Tehran also has little chance of defeating the US military, but escalation may again favour the enemy, according to Prof Robert Pape, director of the University of Chicago Project on Security and Threats, and the author of Bombing to Win: Air Power and Coercion in War.

"Horizontal escalation occurs when a state widens the geographic and political scope of a conflict rather than intensifying it vertically in a single theatre," he says in an essay published in Foreign Affairs, the journal of the US Council on Foreign Relations.

"It is especially appealing as a strategy for the weaker parties in a military contest. Instead of trying to defeat a stronger adversary head-on, the weaker side multiplies arenas of risk " drawing additional states, economic sectors, and domestic publics into the remit of the conflict".